Animation Mecanim - Parts of model displaces after animating

Hi all,

So, I am pretty new to animating in Unity and using Mecanim.

I had a model created in Maya (animated using simple scale/ rotation over pivot points and NOT IK or joints) imported as an FBX into Unity but whenever I tried to make a transition between two animation states of the same model (all model animations were done at 0, 0, 0 in Maya), parts of the model keep displacing themselves out of the body of my character - e.g. the eyes, that were animated using their pivot points.

Any ideas on where the fix should be at (in Maya or Unity)? Or should I be grouping all my animated parts in Maya so that they are imported in at the origin?